How could I fix artifacts caused by the armature modifier "Preserve volume" option
Once I weight paint again I can get rid of what you show in your video so I think it's all a quetion of good weight painting.
See the bones that are on this bone layer, they are the ones that deform your mesh:

Select your armature, shift select the mesh, switch to Weight Paint mode, then select one bone after the other and look at their influence on the mesh, for each of those bones the influence goes too far, you need to correct this:

Make sure that you are in Subtract mode and that you can paint through (the good settings below):

Once done it seems to work fine: